Problem 1 A block of mass m 1.0 kg is sent up by the spring which is compressed

Question

Problem 1 A block of mass m 1.0 kg is sent up by the spring which is compressed by z 10.0 cm. Its path is on the frictionless surface until it reaches the horizontal section CD of length 20.0 m with the coefficient of the kinetic friction uk 0.2. The indicated heights are H 2 m and h 1.0 m, and both springs have the same spring constant k 10 N/m. Figure 3: Problem 1. (a) What is the speed of the block at point A? (2pt) (b) What is the speed of the block at point B (3pt) (c) What is the speed of the block at point C? (3pt) (d) at is the kinetic energy of the block at point D? (6pt) (e) On its return trip, where between points C and D will the block stop? (6pt) Bonus: What should be the compression length of the left spring for a block to slide up just to point B? (3pt)

Explanation / Answer

Part A)

By conservation of energy

PE = KE

.5kx2 = .5mv2

(1 X 104)(.1)2 = (1)v2

v = 10 m/s

Part B)

KE = KE + PE

.5(1)(10)2 = .5(1)(v2) + (1)(9.8)(2)

v = 7.80 m/s

Part C)

KE = KE + PE

.5(1)(10)2 = .5(1)(v2) + (1)(9.8)(1)

v = 8.97 m/s

Part D)

KE - Wf = KE

(.5)(1)(8.97)2 - (.2)(1)(9.8)(20) = .5(1)(v2)

v = 1.41 m/s

Part E)

.5mv2 = umgd

(.5)(1)(1.41)2 = .2(1)(9.8)(d)

d = .510 m (51 cm) away from D

Bonus

mgh + umgd = .5kx2

(1)(9.8)(1) + (.2)(1)(9.8)(20) = .5(1 X 104)x2

x = .099 m

That is 9.9 cm

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